Aimed at the simulation, design, and interpretation of advanced pulse experiments crossing the boundaries between nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR), including the rapidly emerging, hybrid discipline of pulsed dynamic nuclear polarisation (DNP), we present a host of novel features in the widely used SIMPSON software package addressing these aspects. Along with this come new features for advanced pulse sequence evaluation in terms of propagator splitting, high-order spin operator cross terms, and pulse phase transients. These fundamental new tools are introduced in a C++-based next generation of the SIMPSON software, which improves calculations speed in some aspects, is better prepared for further developments, and facilitates easier community contributions to the open-source software package.
In addition to the significant developments in magnetic resonance instrumentation and advances in fundamental theoretical descriptions, versatile numerical simulation tools presented in advanced software packages have played an invaluable role in development, understanding, and application of methods in magnetic resonance. This is pertinent to nuclear magnetic resonance (NMR) and nuclear magnetic resonance imaging (MRI). However, with the development of fast waveform generators and powerful pulsed microwave amplifiers, this also applies increasingly to electron paramagnetic resonance (EPR; or electron spin resonance, ESR) and dynamic nuclear polarisation (DNP). Complementing a large variety of stand-alone programmes, specialised aspects of numerical simulations, and data processing software, several more general software packages have been developed for numerical simulation of advanced NMR pulse sequences: ANTIOPE [1]; Gamma [2]; SIMPSON [3]; wSolids [4]; DMfit [5]; SPINEVO-LUTION [6]; Spinach [7]; SpinDynamica [8]; MolSpin [9]; ssNake [10]; MRSimulator [11]; Sleepy [12]. Each software package has its particular features and strengths, which are not addressed specifically in this work, except by noting that the software packages SIMPSON (simulation package for solidstate NMR spectroscopy) and Spinach probably feature the most general aspects of numerical simulation in solid-state NMR. Likewise, software has been presented for the simulation of EPR spectra and pulse sequences; regarding pulse sequences in particular, attention should be drawn to the general and widely used software package EasySpin [13,14] and components in Spinach [7]. Both of these are also relevant for the simulation of DNP experiments, as are Gamma [2] and SPINEVOLUTION [6]. Furthermore, more specific software for DNP has been introduced recently, including DNPSoup [15]. Our focus in this work is SIMPSON which, since its introduction to the NMR community in 2000, has been one of the most widely used and extensively cited software packages for solid-state NMR. Since the first publication and release as open-source software [3], numerous papers have been presented with each introducing new features: parallelization [16]; optimal control [17,18]; auxiliaries including determination of spin systems (SIMMOL) [19]; efficient powder averaging [20,21]; optimisation of experiments for studies of membrane proteins in oriented lipid bilayers [22]; integration with other software such as EasyNMR [23,24] for easier fitting of experimental data. A number of reviews and special aspects have also been published [25][26][27][28].
EPR is primarily concerned with electron spin dynamics and is theoretically similar to NMR, although electron dynamics occur on different time-scales to nuclear dynamics due to significantly stronger electron spin interactions. An interesting hybrid of EPR and NMR is the emerging field of DNP, which utilises the benefits of EPR to enhance information content and sensitivity of NMR. This extension of SIMPSON incorporates electron spin dynamics features to enable simulation of pulsed EPR and DNP experiments; however, in its present form, it does not include all aspects of EPR found in more extensive simulation packages such as EasySpin [13,14]. It should be noted that many modalities of quantum technologies, in particular quantum sensing, exploit unpaired electron (or exciton) and nuclear spins; this implies that software enabling NMR, EPR, and DNP simulations, as proposed here, may find important applications outside these specific disciplines.
The demands dictated by the simultaneous needs for efficiency, accuracy, and versatility in simulation have increased as experiments have become more sophisticated and the effectiveness of NMR, EPR, and DNP hardware has improved. The most recent major release of SIMPSON, version 4.0 [16], focussed on mitigating these numerical demands and was highly efficient in spin dynamics calculations. However, that was more than a decade ago; an interval equivalent to a century in the current computing age. We note that an intermediate version, SIMPSON version 5.0, was developed to enable optimal control design of experiments optimising for timedependent radio-frequency inhomogeneity [29,30]. In addition to enabling numerical simulation of EPR and DNP pulse sequences, this new major release of SIMPSON, version 6.0, includes an improvement in efficiency of numerical calculation for spin dynamics based in the area of propagator splitting [31] to perform rotations and time-propagation operations, directly addressing the computational overhead inherent in simulating complex multi-spin ensembles. A primary bottleneck in magnetic resonance simulations arises during the time-evolution of the density matrix, particularly within iterative procedures like optimal control. Such tasks necessitate the repeated evaluation of matrix exponentials, a process that becomes prohibitively expensive as the dimensionality
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